We study the natural inclusions of Cb(X)⊗A into Cb(X,A) and
Cb(X,Cb(Y)) into Cb(X×Y). In particular, excepting
trivial cases, both these maps are isomorphisms only when X and
Y are pseudocompact. This implies a result of Glicksberg showing
that the Stone-Čech compactificiation β(X×Y) is
naturally identified with βX × βY if and only if X and
Y are pseudocompact.